Find the gradient of the straight line with the equation 7x+4y+2=0and find the intercepts on the x and y-axis.

Step-by-step explanation:

Given that

7x+4y+2=0

There are two ways to find the slope or gradient if the graph

1. Find the derivative with respect to x

2. Or comparing the equation to equation of a line y=mx+c

Using the first step

7x+4y+2=0

Differentiating with respect to x

7+4dy/dx+0=0

4dy/dx=-7

Then, dy/dx=-7/4

The slope is - 7/4

2. Using the equation of a line

7x+4y+2=0

Let rearrange the equation and make y the subject of the formular

4y=-7x-2

Divide through by 4

4y/4 = (-7x/4) - (2/4)

y=-7/4 x - 1/2

Comparing this to equation of a line y=mx+c,

Then m=-7/4. And the intercept c=-1/2

Now find intercept on x axis

The intercept on axis x means at y=0

Then

7x+4y+2=0

y=0

7x+0+2=0

7x=-2

Then, x=-2/7.

The intercept on the x axis is - 2/7

Also intercept on y axis, i. e. at x=0

7x+4y+2=0

0+4y+2=0

4y+2=0

4y=-2

y=-2/4

y=-1/2.

Then intercept on the y axis is - 1/2