Question

a line passes through the point (1, 3) and has a slope of 5. write an equation in slope - intercept form for this line.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Substitute given values

We know that $m = 5$, and the line passes through the point $(x = 1,y = 3)$. Substitute these values into $y=mx + b$: $3=5\times1 + b$.

Step3: Solve for $b$

$3 = 5 + b$, then $b=3 - 5=-2$.

Step4: Write the equation

Substitute $m = 5$ and $b=-2$ back into $y = mx + b$. The equation of the line is $y = 5x-2$.

Answer:

$y = 5x - 2$