Question

Find the equation of this line. y= [?]x+[?]

Answer 1

Answer:

$y=3x-4$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x=0)

1) Determine the slope (m)

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

On the graph, two points are highlighted for us: (0,-4) and (2,2). Plug these into the formula:

$m=\displaystyle\frac{2-(-4)}{2-0}\\\\m=\displaystyle\frac{2+4}{2}\\\\m=\displaystyle\frac{6}{2}\\\\m=3$

Therefore, the slope of the line is 3. Plug this into $y=mx+b$:

$y=3x+b$

2) Determine the y-intercept (b)

$y=3x+b$

Recall that the y-intercept occurs when x=0. Given the point (0,-4), the y-intercept is therefore -4. Plug this into $y=3x+b$:

$y=3x+(-4)\\y=3x-4$

I hope this helps!