What is an equation of the line that passes through the points (3,4) and (−4,−3)? Put your answer in fully reduced form
1 answer:
Answer:
The equation of the line is y = x + 1
Step-by-step explanation:
The equation of the line is y = m x + b, where
- m is the slope of the line
- b is the y-intercept
The rule of the slope of the line is m = , where
- (x1, y1) and (x2, y2) are two points on the line
∵ The line passes through points (3, 4) and (-4, -3)
∴ x1 = 3 and y1 = 4
∴ x2 = -4 and y = -3
→ Substitute them in the rule of the slope above to find it
∵ m = =
= 1
∴ m = 1
→ Substitute it in the form of the equation above
∴ y = 1(x) + b
∴ y = x + b
→ To find b substitute x by 3 and y by 4 in the equation
∵ 4 = 3 + b
→ Subtract 3 from both sides
∵ 4 - 3 = 3 - 3 + b
∴ 1 = b
→ Substitute it in the equation
∴ y = x + 1
∴ The equation of the line is y = x + 1
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Hope this helps!