Given an equation in point-slope form, explain how

SHRIKETH DORANALA

SHRIKETH DORANALA

Answered question

2022-07-20

Given an equation in point-slope form, explain how to determine the coordinates of its y-intercept.

Answer & Explanation

xleb123

xleb123

Skilled2023-05-24Added 181 answers

In order to determine the coordinates of the y-intercept for an equation given in point-slope form, we need to understand the definition of the y-intercept and the structure of the point-slope form.
The point-slope form of a linear equation is given by:
yy1=m(xx1)
where:
- (x1,y1) represents a point on the line, and
- m represents the slope of the line.
The y-intercept of a line is the point where the line intersects the y-axis. At the y-intercept, the x-coordinate is 0. Therefore, to find the coordinates of the y-intercept, we substitute x=0 into the equation and solve for y.
Let's demonstrate this process step by step using an example equation in point-slope form.
Example equation: y3=2(x2)
Step 1: Substitute x=0 into the equation:
y3=2(02)
Step 2: Simplify the expression:
y3=2(2)
y3=4
Step 3: Isolate y by adding 3 to both sides of the equation:
y=4+3
y=1
Therefore, the coordinates of the y-intercept for the given equation are (0, -1).
In general, for any equation in point-slope form, substituting x=0 into the equation and solving for y will give us the coordinates of the y-intercept.

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