Question

What is the slope-intercept equation of the line that includes (0, 7) and (3, 10)? A. y = 7x – 1 B. y = x – 7 C. y = x + 7 D. y = 7x + 1

Answer 1

To find the equation of the line that passes through 2 points, we have to find the slope and the y-intercept

The form of the equation is y = mx + b

m is the slope

b is the y-intercept

The rule of the slope is

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

Since the line passes through points (0, 7) and (3, 10), then

x1 = 0 and x2 = 3

y1 = 7 and y2 = 10

$\begin{gathered} m=\frac{10-7}{3-0} \\ m=\frac{3}{3} \\ m=1 \end{gathered}$

Substitute m in the rule of the equation

$\begin{gathered} y=1(x)+b \\ y=x+b \end{gathered}$

Since b is the y-intercept (value y at x = 0)

Since the line passes through the point (0, 7), then

b = 7

The equation of the line is

$y=x+7$

The answer is C