What's the y-intercept of 2x + 3y = 24?
The y-intercept is 8, found by setting x = 0: 0 + 3y = 24 → y = 8.
That’s the point (0, 8) on the line. If you're sketching it out, that's where the line meets the y-axis. For a deeper understanding of intercepts, check out why the letter B is used for the y-intercept.
What's the y-intercept of 2x + 8y = 24?
The y-intercept is (0, -3) — plug in x = 0: 2(0) − 8y = 24 → −8y = 24 → y = −3.
So the line crosses the y-axis below the origin at y = -3. Always good to double-check your algebra by solving for y when x = 0.
How do you find a y-intercept?
Set x = 0 and solve for y in the equation of the line.
Take 2x + 5y = 10 as an example: set x = 0 → 5y = 10 → y = 2. That’s your y-intercept: (0, 2). It’s just where the line touches the y-axis. In my experience, labeling the y-intercept early helps when graphing lines by hand. For step-by-step guidance, explore how to find a y-intercept with two points.
What's the slope of 3x + 8y = 24?
The slope is 0.375, found by rearranging to y = (3/8)x − 3.
That’s 3/8, which means a gentle upward tilt. The slope tells you how much y changes for each step right — here, y rises 0.375 for every unit increase in x. For a deeper dive, Khan Academy’s slope guide walks through this step-by-step.
What's the y-intercept of the line y = 3x?
The y-intercept is 0 — the equation is y = 3x + 0.
This line runs straight through the origin (0, 0). It’s a diagonal line with no vertical shift up or down.
How do you write 5x + 3y = 15 in slope-intercept form?
The slope-intercept form is y = (5/3)x + 5 — move 5x to the right and divide by −3.
Here, the slope is 5/3 (about 1.67) and the y-intercept is 5. That’s where the line crosses the y-axis.
What's the solution to this system of linear equations: 2x + 3y = 3 and 7x − 3y = 24?
The solution is (3, -1) — solving simultaneously gives x = 3 and y = -1.
Plug x = 3 and y = -1 into both equations to verify: 2(3) + 3(-1) = 6 - 3 = 3 ✓ and 7(3) - 3(-1) = 21 + 3 = 24 ✓. For more on systems of equations, Purplemath’s guide is a solid reference.
How do you find a y-intercept with two points?
Use the slope and one point to solve for b in y = mx + b.
First find the slope m from the two points. Then plug m and one point into y = mx + b and solve for b, the y-intercept. I’ve found this method especially handy when plotting scatter plots and drawing trend lines.
How do you find the y-intercept given two points?
Calculate the slope, then use it with one point to find b in y = mx + b.
For example, with points (3, 5) and (6, 11): slope m = (11 − 5)/(6 − 3) = 2. Then use 5 = 2(3) + b → b = −1. So the y-intercept is −1. Learn more about finding y-intercepts with two points.
Can you give me a y-intercept example?
The y-intercept is the y-value where the line crosses the y-axis, often given as a single number like 3.5.
In y = mx + b, b is the y-intercept. For instance, in y = −2x + 4, the y-intercept is 4 — the line crosses the y-axis at (0, 4). According to Britannica, this is a fundamental concept in coordinate geometry.
What's the slope for 8y = 24?
The slope is 1/8 — divide both sides by 8: y = (1/8)x + 3.
This line rises gently — for every 8 units right, y rises 1 unit. The coefficient of x is the slope.
What's the factor of 8y = 24?
The GCF of 8y and 24 is 8 — both terms are divisible by 8.
Factoring out 8 gives 8(y + 3). This simplifies the expression and helps solve for intercepts or roots. Math is Fun’s factoring page offers a clear breakdown of this process.
What's the slope of 8y = 24?
The slope is 1/8 — rewrite as y = (1/8)x + 3.
Since there’s a constant term, the y-intercept is 3. The line has a gentle upward slope.
What's the y-intercept of 3x + 4y = -24?
The y-intercept is (0, -6) — set x = 0: 4y = -24 → y = -6.
This is the point where the line crosses the y-axis. Always plug x = 0 into the equation to find it. As a quick check, Varsity Tutors explains why this works.
What's the y-intercept of y = -3x + 2?
The y-intercept is (0, 2) — the equation is y = -3x + 2.
The constant term 2 tells you exactly where the line hits the y-axis. Use this to sketch the graph quickly. For a refresher on linear equations, Khan Academy’s linear equations section is a great place to start.
What's the y-intercept of 2x + 3y = 24?
The y-intercept is 8 — set x = 0 and solve for y.
This gives us the point (0, 8) on the y-axis. Honestly, this is one of the easiest intercepts to find.
What's the Y intercept of 2x - 8y = 24?
The y-intercept is -3 — set x = 0 and solve for y.
That lands us at (0, -3) on the graph. Always good to verify by plugging back in.
What's the slope of 3x - 8y = 24?
The slope is 0.375 — rearrange to y = (3/8)x - 3.
That’s 3/8, which is a gentle incline. The slope tells the story of how steep the line is.
What's the y-intercept of the line 3x?
The y-intercept is 0 — since there's no constant term.
This line passes right through the origin (0,0). It's a simple diagonal line.
What is 5x + 3y = 15 in slope-intercept form?
The slope-intercept form is y = -(5/3)x + 5 — rearrange the equation.
Here the slope is -5/3 and the y-intercept is 5. That's where the line crosses the y-axis.
What's the solution to this system of linear equations: 2x + 3y = 3 and 7x - 3y = 24?
The solution is (3, -1) — solving both equations together.
Plugging those values back in confirms they work for both equations. A solid example of solving systems.
What is a y-intercept example?
The y-intercept is where the line crosses the y-axis, like 3.5 in many equations.
In y = mx + b, b is the y-intercept. For y = -2x + 4, it's 4. That's the point (0,4).
What's the slope for 8y = 24?
The slope is 1/8 — divide both sides by 8.
This gives y = (1/8)x + 3. The slope is the coefficient of x.
What's the factor of 8y = 24?
The GCF is 8 — both 8y and 24 divide evenly by 8.
Factoring out 8 gives 8(y + 3). This simplifies the equation nicely.
What's the slope of 8y = 24?
The slope is 1/8 — rewrite the equation as y = (1/8)x + 3.
The slope is the coefficient of x, and the y-intercept is 3.
What's the y-intercept of 3x + 4y = -24?
The y-intercept is -6 — set x = 0 and solve for y.
That's the point (0, -6) on the graph. Always verify by plugging back in.
What's the y-intercept of y = -3x + 2?
The y-intercept is 2 — it's the constant term in the equation.
This means the line crosses the y-axis at (0, 2). Super straightforward to find.
