Question

Find the slope of a line which passes through a point A (5.-3) and meets y
axis at 7.​

Answer 1

Given,

A line passes through point A(5.-3) and meets the y-axis at 7.

To Find,

The slope of the line.

Solution,

Since it is given that the line meets the y-axis at 7

So, the coordinates of that point will be (0,7)

Now, the formula for calculating the slope of a line if two points are given is

m = (y₂-y₁)/(x₂-x₁)

where, y₂ = 7, y₁ = -3, x₂ = 0, and x₁ = 5

m = (7+3)/(0-5)

m = 10/-5

m = -2.

Hence, the slope of the line is -2.

Answer 2

We need to recall the concept of the slope of a straight line.

If a line passes through the points $(x_1,y_1)$,  and  $(x_2,y_2)$ , then the slope of the line is $m=\frac{y_2-y_1}{x_2-x_1}$ .

Given:

A line passed through the point $A(5,-3)$.

The line intersects the y-axis at $7$.

The line passes through the points $(5,-3)$ and $(0,7)$.

Using the slope formula, we get

$m=\frac{7-(-3)}{0-5}$

$m=\frac{10}{-5}$

$m=-2$

Thus, the slope of the line is $-2$.