Question

Question 8: Find the equation of the straight line that:

(a) has a gradient of 4 and passes through the point (1, 10)

Answer 1

answer = y = 4x + 6

y = mx + b

gradient = slope = m = 4

(1,10) = (x,y)

plug in the values

10 = 4 (1) + b

10 = 4 + b

b = 6

y = 4x + 6

Answer 2

`y=4x+6`

Explanation:

Hi there!

Linear equations are typically organized in slope-intercept form:
`y=mx+b` where m is the slope (also called the gradient) and b is the y-intercept (the value of y when x is 0)

1) Plug the gradient into the equation (b)

`y=mx+b`

We're given that the gradient of the line is 4. Plug this into
`y=mx+b` as m:

`y=4x+b`

2) Determine the y-intercept (b)

`y=4x+b`

Plug in the given point (1,10) as (x,y) and solve for b

`10=4(1)+b\\10=4+b`

Subtract 4 from both sides to isolate b

`10-4=4+b-4\\6=b`

Therefore, the y-intercept of the line is 6. Plug this back into
`y=4x+b` as b:

`y=4x+6`

I hope this helps!