Photo AI

Find the equation of the line passing through the point $(-2, -3)$ which is parallel to the line with equation $y + 4x = 7$. - Scottish Highers Maths - Question 1 - 2016

Question icon

Question 1

Find-the-equation-of-the-line-passing-through-the-point-$(-2,--3)$-which-is-parallel-to-the-line-with-equation-$y-+-4x-=-7$.-Scottish Highers Maths-Question 1-2016.png

Find the equation of the line passing through the point $(-2, -3)$ which is parallel to the line with equation $y + 4x = 7$.

Worked Solution & Example Answer:Find the equation of the line passing through the point $(-2, -3)$ which is parallel to the line with equation $y + 4x = 7$. - Scottish Highers Maths - Question 1 - 2016

Step 1

Find the gradient

96%

114 rated

Answer

To find the gradient of the line given by the equation y+4x=7y + 4x = 7, we first rearrange it into slope-intercept form, y=mx+by = mx + b, where mm is the gradient.

Starting with the original equation: y+4x=7y + 4x = 7 Subtracting 4x4x from both sides gives: y=−4x+7y = -4x + 7 Thus, the gradient (slope) of the line is m=−4m = -4.

Step 2

State equation

99%

104 rated

Answer

Since we need to find the equation of the line that is parallel to this line and passes through the point (−2,−3)(-2, -3), we use the same gradient m=−4m = -4.

Using the point-slope form of the line: y−y1=m(x−x1)y - y_1 = m(x - x_1) where (x1,y1)=(−2,−3)(x_1, y_1) = (-2, -3), we have: y−(−3)=−4(x−(−2))y - (-3) = -4(x - (-2)) This simplifies to: y+3=−4(x+2)y + 3 = -4(x + 2) Distributing gives: y+3=−4x−8y + 3 = -4x - 8 Finally, rearranging to standard form leads to: y+4x=−5.y + 4x = -5.

Join the Scottish Highers students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;