Question

Write the slope-intercept form of the equation of the line through the given points.

Answer 1

Answer:  y = 3x+4

Slope = 3

y intercept = 4

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Explanation:

Let's find the slope.

$m = \text{slope}\\\\m=\frac{\text{rise}}{\text{run}}\\\\m = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{7-4}{1-0}\\\\m = \frac{3}{1}\\\\m = 3$

The slope is m = 3.

The y intercept is b = 4 due to the point (0,4). The y intercept always occurs when x = 0.

We'll then plug those m and b values into y = mx+b to get the answer y = 3x+4

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As a way to check the answer, plugging x = 0 should lead to y = 4

y = 3x+4

y = 3*0+4

y = 0+4

y = 4

So that works out. Let's try x = 1. It should produce y = 7

y = 3x+4

y = 3*1+4

y = 3+4

y = 7

That works out also. The answer is fully confirmed.