Write the equation of a line parallel to y = 1/2x + 8 that passes through ( 4, 9 ).

y = x/2 + 7

Step-by-step explanation:

The equation of a line, represented in the slope-intercept form, is

y = mx + c

Where

Slope = m

c = intercept

Looking at the equation given,

y=1/2x + 8

Slope,m = 1/2

If a line is parallel to a another line, then the slope of one line is equal to the slope of the other line. It means that the slope of the parallel line that passes ( 4, 9 ) will be 1/2

To determine c,

We will substitute m = 1/2, y = 9 and x = 4 into the slope intercept equation,

y = mx + c. It becomes

9 = 1/2 × 4 + c

9 = 2 + c

c = 9- 2= 7

The equation becomes

y = x/2 + 7

b. 2

step-by-step explanation:

the slope of a line =δy/δx

δy= y₂-y₁

δx= x₂-x₁

therefore, using the points (-2,-3)   and (3,7) we can calculate gradient as follows:

m=(7--3)/(3--2) (a number minus a negative number the sign changes to a plus)

m=(7+10)/(3+2)

=10/5

=2