Worksheet on writing equations of lines, including slope-intercept and point-slope forms with graphical representations.

Let’s solve each problem one by one.

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Problem 1:

We are given a graph of a line and need to write its equation in slope-intercept form:
> y = mx + b, where m is the slope, and b is the y-intercept.

From the graph:
- The line crosses the y-axis at (0, -2) → so b = -2
- To find slope (m), pick two points on the line. Let’s use:
- Point A: (0, -2)
- Point B: (-5, 5) — looks like it passes through there? Wait, let me check again.

Actually, looking carefully:

At x = 0, y = -2 → that’s clear.

At x = -5, y = 5? Let’s count grid units.

From (0, -2) going left 5 units (to x = -5), we go up 7 units → to y = 5. So yes, point (-5, 5) is on the line.

So slope m = rise/run = (5 - (-2)) / (-5 - 0) = 7 / (-5) = -7/5

So equation: y = (-7/5)x - 2

That matches option C

✔ Check: Plug in x=0 → y=-2 ✔️
Plug in x=-5 → y = (-7/5)(-5) - 2 = 7 - 2 = 5 ✔️

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Problem 2:

Graph shows a line with positive slope.

Y-intercept: crosses y-axis at (0, 4) → so b = 4

Find another point: when x = 3, y = 6? Let’s see.

From (0,4) to (3,6): rise = 2, run = 3 → slope = 2/3

Equation: y = (2/3)x + 4

That’s option C

✔ Check: x=0 → y=4 ✔️
x=3 → y=(2/3)*3 + 4 = 2+4=6 ✔️

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Problem 3:

“through: (2, 4), parallel to y = 3x - 3”

Parallel lines have same slope.

Slope of given line: m = 3

Point-slope form: y - y₁ = m(x - x₁)

Plug in: y - 4 = 3(x - 2)

That’s option B

✔ Correct.

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Problem 4:

“through: (1, -4), parallel to x = 0”

x = 0 is the y-axis — a vertical line.

A line parallel to a vertical line is also vertical.

Vertical line through (1, -4) has equation: x = 1

But none of the options say x = 1 directly.

Look at options:

A) y + 4 = -3(x + 1) → not vertical
B) y + 1 = 3(x + 4) → not vertical
C) 0 = x - 1 → which means x = 1 ← this is correct!
D) y + 4 = 0 → horizontal line y = -4

So answer is C

✔ Because 0 = x - 1 → x = 1

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Problem 5:

“through: (-5, -4), perp. to y = -5/6 x - 3”

Perpendicular slopes are negative reciprocals.

Given slope: m = -5/6

Negative reciprocal: flip fraction and change sign → 6/5

Point-slope form using point (-5, -4):

y - (-4) = (6/5)(x - (-5))
→ y + 4 = (6/5)(x + 5)

That’s option D

✔ Check: slope is 6/5, point (-5,-4) plugged in correctly.

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Problem 6:

“through: (5, -5), perp. to y = 5/8 x - 3”

Given slope: 5/8

Perpendicular slope: negative reciprocal → -8/5

Point-slope form using (5, -5):

y - (-5) = (-8/5)(x - 5)
→ y + 5 = (-8/5)(x - 5)

That’s option C

✔ Correct.

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Final Answers:

1) C
2) C
3) B
4) C
5) D
6) C

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Final Answer:
1) C
2) C
3) B
4) C
5) D
6) C