What is the equation of the line described below written in slope-intercept form? the line passing through point (2, 4), parallel to the line whose equation is y = x

if it helps, y = x can be written as y = 1x + 0.....here ur slope is 1. A parallel line will have the same slope

y = mx + b
slope(m) = 1
(2,4)...x = 2 and y = 4
now we sub and find b, the y int
4 = 1(2) + b
4 = 2 + b
4 - 2 = b
2 = b

so ur parallel equation is : y = x + 2

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ColinJacobus ColinJacobus · Answer 2 · 2019-07-24T13:28:27-04:00

Answer: The required equation of the line in slope-intercept form is \(y=x+2.\)

Step-by-step explanation: We are given to find the slope-intercept form of the equation of a line passing through the point (2, 4), parallel to the line with the following equation :

\(y=x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)

We know that

the slope-intercept form of the equation of a line with slope m and y-intercept c is given by

\(y=mx+c.\)

From equation (i), we have

\(y=x\\\\\Rightarrow y=1\times x+0.\)

Comparing with the slope-intercept form, we get

slope of line (i) is m = 1.

Since the slopes of two parallel lines are equal, so the slope of the new line will be

\(m=1.\)

Also, the line passes through the point (2, 4), so its equation will be

\(y-4=m(x-2)\\\\\Rightarrow y-4=1\times(x-2)\\\\\Rightarrow y-4=x-2\\\\\Rightarrow y=x-2+4\\\\\Rightarrow y=x+2.\)

Thus, the required equation of the line in slope-intercept form is \(y=x+2.\)