Slope and Slope Intercept Form Worksheet | PDF | Equations ... - Free Printable

Here are the solutions to the problems on your worksheet.

1) Find the slope of the line through each pair of points.

Formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

a. Points: $(8, -7)$ and $(5, -3)$
* Subtract the y-values: $-3 - (-7) = -3 + 7 = 4$
* Subtract the x-values: $5 - 8 = -3$
* Slope ($m$): $\frac{4}{-3} = -\frac{4}{3}$

b. Points: $(-5, 9)$ and $(5, 11)$
* Subtract the y-values: $11 - 9 = 2$
* Subtract the x-values: $5 - (-5) = 5 + 5 = 10$
* Slope ($m$): $\frac{2}{10}$ (simplify by dividing top and bottom by 2) $= \frac{1}{5}$

c. Points: $(-8, -4)$ and $(-4, -9)$
* Subtract the y-values: $-9 - (-4) = -9 + 4 = -5$
* Subtract the x-values: $-4 - (-8) = -4 + 8 = 4$
* Slope ($m$): $\frac{-5}{4} = -\frac{5}{4}$

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2) Write the equation of the line in SLOPE-INTERCEPT FORM

Form: $y = mx + b$ (where $m$ is slope and $b$ is the y-intercept).

Top Row Graphs:
* Left Graph: The line crosses the y-axis at $+2$. To get to the next clear point, go down 1 and right 2. Slope is $-\frac{1}{2}$.
* Equation: $y = -\frac{1}{2}x + 2$
* Middle Graph: The line crosses the y-axis at $0$. To get to the next clear point, go up 3 and right 2. Slope is $\frac{3}{2}$.
* Equation: $y = \frac{3}{2}x$
* Right Graph: The line crosses the y-axis at $-2$. To get to the next clear point, go down 1 and right 4. Slope is $-\frac{1}{4}$.
* Equation: $y = -\frac{1}{4}x - 2$

Bottom Row Graphs:
* Left Graph: The line crosses the y-axis at $-2$. To get to the next clear point, go up 3 and right 2. Slope is $\frac{3}{2}$.
* Equation: $y = \frac{3}{2}x - 2$
* Middle Graph: The line crosses the y-axis at $+3$. To get to the next clear point, go down 2 and right 2. Slope is $\frac{-2}{2} = -1$.
* Equation: $y = -1x + 3$ (or just $y = -x + 3$)
* Right Graph: The line crosses the y-axis at $+1$. To get to the next clear point, go up 2 and right 3. Slope is $\frac{2}{3}$.
* Equation: $y = \frac{2}{3}x + 1$

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3) Identify the slope (m) and the y-intercept (b)

Goal: Rewrite equations into $y = mx + b$ form if needed.

a. $y = 4x - 5$
* Already in correct form.
* $m = 4$, $b = -5$

b. $y = 11 + \frac{2}{3}x$
* Rearrange: $y = \frac{2}{3}x + 11$
* $m = \frac{2}{3}$, $b = 11$

c. $y = \frac{2}{3} - x$
* Rearrange: $y = -1x + \frac{2}{3}$
* $m = -1$, $b = \frac{2}{3}$

d. $6 - \frac{9}{2}x = y$
* Flip it around: $y = -\frac{9}{2}x + 6$
* $m = -\frac{9}{2}$, $b = 6$

e. $y = \frac{5}{2}x - \frac{19}{8}$
* Already in correct form.
* $m = \frac{5}{2}$, $b = -\frac{19}{8}$

f. $-\frac{5}{4} - \frac{2}{7}x = y$
* Flip it around: $y = -\frac{2}{7}x - \frac{5}{4}$
* $m = -\frac{2}{7}$, $b = -\frac{5}{4}$

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4) Find the equation of the line in slope-intercept form

*(Note: The specific problem text for question #4 was cut off at the bottom of the image, so it cannot be solved here. However, the method is usually: find the slope between two points, then plug one point and the slope into $y = mx + b$ to solve for $b$.)*

Final Answer:

1) Slopes:
a. $-\frac{4}{3}$
b. $\frac{1}{5}$
c. $-\frac{5}{4}$

2) Equations:
* Top Left: $y = -\frac{1}{2}x + 2$
* Top Middle: $y = \frac{3}{2}x$
* Top Right: $y = -\frac{1}{4}x - 2$
* Bottom Left: $y = \frac{3}{2}x - 2$
* Bottom Middle: $y = -x + 3$
* Bottom Right: $y = \frac{2}{3}x + 1$

3) Slope (m) and Y-intercept (b):
a. $m = 4$, $b = -5$
b. $m = \frac{2}{3}$, $b = 11$
c. $m = -1$, $b = \frac{2}{3}$
d. $m = -\frac{9}{2}$, $b = 6$
e. $m = \frac{5}{2}$, $b = -\frac{19}{8}$
f. $m = -\frac{2}{7}$, $b = -\frac{5}{4}$