graph a linear function with the given slope and y - intercept. slope: 3, y - intercept: 10

Answer

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear function is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $m = 3$ and $b = 10$, the equation of the line is $y=3x + 10$.

Step2: Analyze the y - intercept

The y - intercept is 10, so the line crosses the y - axis at the point $(0,10)$. All the graphs have the line crossing the y - axis at 10, so we move to the slope analysis.

Step3: Analyze the slope

The slope $m = 3=\frac{3}{1}$, which means for every 1 unit increase in $x$, $y$ increases by 3 units. A positive slope means the line is increasing from left to right.

Step4: Check the options

Option A has a line with a positive slope and y - intercept of 10. Options B and C have negative slopes. Option D has a slope that is less steep than what we need for a slope of 3.