Question

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

Answer 1

Answer:

$y=4x+6$

Step-by-step 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!

Answer 2

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