Question

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

Answer 1

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

Answer 2

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 $y=x+2.$