Slope and y-intercept graphing worksheet for algebra practice.

Let’s solve each problem step by step. We’re graphing linear equations on a coordinate plane. Each equation is in the form y = mx + b, where:

- m is the slope (how steep the line is)
- b is the y-intercept (where the line crosses the y-axis)

We’ll find two points for each line, plot them, and draw the line through them.

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Problem 1: Graph y = -3x + 2

Step 1: Find the y-intercept → when x = 0, y = -3(0) + 2 = 2
→ Point A: (0, 2)

Step 2: Pick another x-value, say x = 1 → y = -3(1) + 2 = -1
→ Point B: (1, -1)

Plot these two points and draw a straight line through them.

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Problem 2: y = ½x + 4

Step 1: y-intercept → x = 0 → y = ½(0) + 4 = 4
→ Point A: (0, 4)

Step 2: Let x = 2 → y = ½(2) + 4 = 1 + 4 = 5
→ Point B: (2, 5)

Plot and connect.

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Problem 3: y = 2.60x

This is y = 2.6x + 0 → y-intercept is 0.

Step 1: x = 0 → y = 0 → Point A: (0, 0)

Step 2: x = 1 → y = 2.6 → Point B: (1, 2.6) — that’s between 2 and 3 on y-axis.

You can also use x = 5 → y = 13 → but grid only goes to ±10, so maybe x = 3 → y = 7.8 → still okay.

Use (0,0) and (1, 2.6). Draw line through origin with positive slope.

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Problem 4: y = 2/3 x + 5

Step 1: x = 0 → y = 5 → Point A: (0, 5)

Step 2: Use slope 2/3 → go up 2, right 3 from (0,5) → new point: (3, 7)

Or pick x = 3 → y = 2/3*(3) + 5 = 2 + 5 = 7 → same point.

Plot (0,5) and (3,7), draw line.

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Problem 5: y = -10x

y-intercept = 0 → Point A: (0, 0)

Pick x = 1 → y = -10 → Point B: (1, -10)

That’s at bottom of grid. You can also use x = -1 → y = 10 → top of grid.

So plot (0,0) and (1,-10) or (-1,10). Line goes steeply downward.

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Problem 6: y = -2.5x + 5

Step 1: x = 0 → y = 5 → Point A: (0, 5)

Step 2: x = 2 → y = -2.5*2 + 5 = -5 + 5 = 0 → Point B: (2, 0)

Perfect! Plot (0,5) and (2,0), draw line.

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Problem 7: y = -¼(x - 2) - 3

First, simplify if needed, or plug in values.

Let’s expand:
y = -¼x + ½ - 3 = -¼x - 2.5

But we can also just plug in x-values.

Step 1: Try x = 2 → y = -¼(0) - 3 = -3 → Point A: (2, -3)

Step 2: Try x = 6 → y = -¼(6-2) - 3 = -¼(4) - 3 = -1 - 3 = -4 → Point B: (6, -4)

Or try x = -2 → y = -¼(-2-2) - 3 = -¼(-4) - 3 = 1 - 3 = -2 → Point C: (-2, -2)

Use (2, -3) and (-2, -2) — easier to plot.

Slope is negative small number — gentle downward slope.

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Problem 8: y = ⅓(2x - 6) + 4

Simplify first:

y = (2/3)x - 2 + 4 = (2/3)x + 2

Now it’s easy!

Step 1: x = 0 → y = 2 → Point A: (0, 2)

Step 2: Use slope 2/3 → go up 2, right 3 → from (0,2) to (3,4)

Check: x=3 → y = (2/3)(3) + 2 = 2 + 2 = 4 → yes.

Plot (0,2) and (3,4), draw line.

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✔ All problems solved by finding two points per line and drawing the line through them.

Final Answer:
Graphs completed using calculated points for each equation as shown above.