Question

What are the gradient and y-intercept of the line `y=4x+3`? Graph the line.

Answer 1

It couldn't be easier! When the equation of a line is written in the form `y = mx+c`, the number `m` - in this case 4 - is the gradient and the number `c` - in this case 3 - is the y-intercept.

Explanation:

A little more explanation

The y-intercept is the point where the line crosses the line `x=0`, which is the y-axis.

If we substitute `x=0` in the equation, we get:

`y=4x+3`

`y = 4(0) +3`

`y = 3`

This is the y-intercept. It is a constant, which is why we use the letter 'c' to represent it, but some books use 'b' so the equation would be `y=mx+b`.

The gradient (sometimes called 'slope') tells us how much the line moves upward in the y direction for each 1 unit it moves along in the x-direction. We use the letter 'm' to represent the gradient. In this case, the gradient is 4: every time we move 1 unit to the right, we move 4 units upward.

Answer 2

`"gradient "=4" and y-intercept "=3`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))`
where m represents the gradient and b the y-intercept.

`y=4x+3" is in this form"`

`rArr"gradient "=m=4" and y-intercept "=b=3`
graph{4x+3 [-10, 10, -5, 5]}