Math

QuestionFind the line equation through points (3,0)(-3,0) and (0,3)(0,3).

Studdy Solution

STEP 1

Assumptions1. The line passes through the points (3,0)(-3,0) and (0,3)(0,3). . We are looking for the equation of the line in the form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is given by the formulam=y2y1x2x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

Now, plug in the given values for the coordinates of the two points to calculate the slope.
m=300(3)m = \frac{3 -0}{0 - (-3)}

STEP 4

Calculate the slope.
m=33=1m = \frac{3}{3} =1

STEP 5

Now that we have the slope, we can find the y-intercept. Since the line passes through the point (0,3)(0,3), the y-intercept is3.

STEP 6

Now, we can write the equation of the line using the slope and the y-intercept.
y=mx+by = mx + b

STEP 7

Plug in the values for the slope and the y-intercept to write the equation of the line.
y=1x+3y =1x +3

STEP 8

implify the equation.
y=x+3y = x +3The equation of the line that passes through the points (3,0)(-3,0) and (0,3)(0,3) is y=x+3y = x +3.

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