Write an equation of the line that passes through (−1,3) and is parallel to the line y=2x+2.

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08-12-2019
Mathematics

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Write an equation of the line that passes through (−1,3) and is parallel to the line y=2x+2.

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iwillanswer iwillanswer · Answer 1 · 2019-12-14T13:45:44+01:00

The equation of the line that passes through (−1,3) and is parallel to the line y = 2x + 2 in slope intercept form is y = 2x + 5

Solution:

Given that line passes through (-1, 3) and parallel to line y = 2x + 2

We have to find the equation of the line

Let us first find the slope of the line

The slope intercept form of line is given as:

y = mx + c ---- eqn 1

where "m" is the slope of the line and "c" is the y-intercept

Comparing the given line equation y = 2x + 2 with y = mx + c,

We get slope "m" = 2

The slope of parallel lines are equal

Hence slope of the line which is parallel to y = 2x + 2 is also 2

Now let us find the equation of line with slope "m" = 2 and passes through point (-1, 3)

Substitute (x, y) = (-1, 3) in eqn 1 to find value of "c"

3 = 2(-1) + c

3 = -2 + c

c = 5

Now substitute "c" = 5 and m = 2 in eqn 1 to get equation of required line

y = 2x + 5

Thus the equation of line in slope intercept form is y = 2x + 5

astha8579 astha8579 · Answer 2 · 2022-02-04T12:39:20+01:00

You can use the fact that parallel lines have same slope and that y = mx + c has "m" as slope.

The equation of the considered line is [tex]y = 2x + 5[/tex]

How to get the slope intercept form of a straight line equation?

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

[tex]y = mx + c[/tex]

How are parallel straight lines related?

Parallel lines have same slope, since slope is like measure of steepness and since parallel lines are of same steepness, thus, are of same slope.

Since given parallel line has equation y = 2x + 2 ,thus its slope is 2 and thus, the slope of the needed line is 2 too.

Thus, equation of the specified line is [tex]y = 2x + c[/tex]

The other data(the point (-1,3) on the line) about the straight line will help us find the value of c.

Since the line passes through (-1,3) coordinate, thus this must satisfy the equation. Putting x = -1, and y = 3 will give us:

[tex]y = 2x + c\\3 = 2 \times -1 + c\\3 + 2 = 5 = c[/tex]

Thus, the value of y-intercept = c = 5

Thus, the equation of the considered line we get is

[tex]y = 2x + 5[/tex]

The graph of this equation is given below.

Learn more about linear equations here:

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