Question

Write the equation of a line parallel to x+4y=3 and passing through the point (8,-4). Explain or show your reasoning

Answer 1

Answer:

The equation is x + 4y + 8 = 0.

Step-by-step explanation:

To find the equation of a line parallel to x+4y=3 and passing through the point (8,-4), we first find the gradient of the given equation by converting it to the slope intercept form.

Slope intercept form: $\boxed{y=mx+c}$

where,

• m = gradient
• c = y intercept

$x+4y=3$

$4y=-x+3$

$\displaystyle y=-\frac{1}{4} x+\frac{3}{4}$

Therefore, the gradient of x+4y=3 is $\bf -\frac{1}{4}$

For parallel lines, they have the same gradient. Therefore, the new equation also has a gradient of $-\frac{1}{4}$

For linear equation with given gradient $(m)$ and 1 point $(x_1,y_1)$, the equation will be:

$\boxed{y-y_1=m(x-x_1)}$

Given:

• $m=-\frac{1}{4}$
• $x_1=8$
• $y_1=-4$

Then, the equation will be:

$y-y_1=m(x-x_1)$

$\displaystyle y-(-4)=-\frac{1}{4} (x-8)$

$-4(y+4)=x-8$

$-4y-16=x-8$

$\bf x+4y+8=0$