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

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

2 Answers

7 votes

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

User Besc
by
8.2k points
0 votes

Answer:


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!

User Szuuuken
by
8.3k points

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