find the equation of the line passing through the points (-5,1) and (5,7). y = \\frac{?}{\\square}x + \\square
find the equation of the line passing through the points (-5,1) and (5,7). y = \\frac{?}{\\square}x + \\square
Answer
Answer:
$\frac{3}{5}x + 4$
Explanation:
Step1: Calculate the slope
The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-5,1)$ and $(x_2,y_2)=(5,7)$. $m=\frac{7 - 1}{5-(-5)}=\frac{6}{10}=\frac{3}{5}$.
Step2: Find the y - intercept
Use the point - slope form $y - y_1=m(x - x_1)$. Take the point $(-5,1)$ and $m = \frac{3}{5}$. $y - 1=\frac{3}{5}(x + 5)$. Expand: $y-1=\frac{3}{5}x+3$. Add 1 to both sides: $y=\frac{3}{5}x + 4$.