Question

Write an equation in slope-intercept form for the following line:

(-17,-4) and (-7,-13)

Answer 1

Slope-intercept form

Linear equations are often organized in slope-intercept form:

$y=mx+b$

• (x,y) = a point that falls on the line
• m = the slope of the line
• b = the y-intercept of the line

Slope (m)

The slope of a line is equal to its $\dfrac{rise}{run}$.

• "Rise" refers to the number of units the line travels up.
• "Run" refers to the number of units the line travels to the right.

Typically, we would solve for the slope by using the following formula:

• $m=\dfrac{y_2-y_1}{x_2-x_1}$ where two points that fall on the line are $(x_1,y_1)$ and $(x_2,y_2)$

Y-intercept (b)

The y-intercept of a line refers to the y-value that occurs when x=0.

On a graph, it is the y-value where the line crosses the y-axis.

Writing the Equation

1) Determine the slope of the line (m)

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Plug in the two given points, (-17,-4) and (-7,-13):

$m=\dfrac{-13-(-4)}{(-7)-(-17)}\\\\m=\dfrac{-13+4}{-7+17}\\\\m=\dfrac{-9}{10}$

Therefore, the slope of the line is $-\dfrac{9}{10}$. Plug this into $y=mx+b$:

$y=-\dfrac{9}{10}x+b$

2) Determining the y-intercept (b)

$y=-\dfrac{9}{10}x+b$

Plug in one of the given points and solve for b:

$-4=-\dfrac{9}{10}(-17)+b\\\\-4=\dfrac{153}{10}+b\\\\b=-\dfrac{193}{10}$

Therefore, the y-intercept of the line is $-\dfrac{193}{10}$. Plug this back into our equation:

$y=-\dfrac{9}{10}x-\dfrac{193}{10}$

Answer

$y=-\dfrac{9}{10}x-\dfrac{193}{10}$