Question

What is the equation of line that passes through $(4,7)$ and has a slope of $0.5$?

Answer 1

If ‘$m$ ’ is the slope of line and it passes through a point $({x_1},{y_1})$, then its equation is written as: $y - {y_1} = m(x - {x_1})$
Given: A point $(4,7)$ through which the line passes and its slope which is equal to $0.5$.
To find: Equation of line with slope .5 and passes through a point $(4,7)$

Complete step-by-step solution:
Step 1: From point slope form we know that the equation of line is given by the equation,
$y - {y_1} = m(x - {x_1})$
Now here it is given that,
${x_1} = 4,{y_1} = 7\& slope(m) = 0.5$
Substituting the values in above equation of line, we get
$y - {y_1} = m(x - {x_1})$
$y - 7 = 0.5(x - 4)$
This form is known as point slope form.
Step 2: rearranging the terms on both side of the above equation
We get,
$y - 7 = 0.5(x - 4)$
$\Rightarrow y = 7 + 0.5(x - 4)$
Step 3: On further simplification, we get
$y = 7 + 0.5(x - 4)$
$\Rightarrow y = 7 + 0.5x - 2$
$\Rightarrow y = 0.5x + 5$
The form of the above obtained equation i.e. $y = 0.5x + 5$is known as slope intercept form.
Hence, the equation of line that passes through a point$(4,7)$and has a slope equal to$0.5$ is,
$y - 7 = 0.5(x - 4)$ Or $y = 0.5x + 5$
Point Slope Form $\;\;\;\;\;$ Slope Intercept Form
Additional information:

If a and b are the intercepts made by a line on the axes of x and y, its equation is written as:
$\dfrac{x}{a} + \dfrac{y}{b} = 1$, this form is known as the Intercept form.
Equation of line passing through two points $({x_1},{y_1})\& ({x_2},{y_2})$ is written as:
$y - {y_1} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}(x - {x_1})$, this form is known as two point form.

Note: These minor details should be noted
$>$ Equation of a line parallel to x-axis at a distance $a$ is $y = a$ or $y = - a$
$>$ Equation of x-axis is $y = 0$
$>$ Equation of line parallel to y-axis at a distance $b$ is $x = b$ or $x = - b$
$>$ Equation of y-axis is $x = 0$