1. Find the equation of the straight line passing through the point (3, -2) and having the same gradient as the line 2y = 5x + 7. NOTEplease give an informative answer

Question

asked Jun 27, 2023 152k views

1 Answer

JonStonecash · Answer 1 · 2023-07-03T10:56:23+0000

Explanation:

Our straight line has the same gradient as that of the line,

2y=5x+7

Dividing each term by 2,

$y=(5)/(2)\,x+(7)/(2)$

Now this equation is in the form
y=mx+c, so the gradient of this line is 5/2.

So the gradient of our straight line is,

m=(5)/(2)

Given our straight line passes through the point,

$(x_1,\ y_1)=(3,\ -2)$

The equation of a straight line passing through a point
$(x_1,\ y_1)$ and having gradient
is given by,

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

This form of equation of a straight line is called point - slope form.

By this point - slope form, the equation of our straight line will be given by,

$\longrightarrow y-(-2)=(5)/(2)\,(x-3)$

$\longrightarrow y+2=(5)/(2)\,(x-3)$

$\longrightarrow2(y+2)=5(x-3)$

$\longrightarrow2y+4=5x-15$

$\longrightarrow\underline{\underline{5x-2y-19=0}}$

This is the equation of our straight line, written in the form
Ax+By+C=0.