Question

a line passes through (1,1) and (-3,5) what is the equation of the line in slope intercept form? y=

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 1}}\quad ,&{{ 1}})\quad % (c,d) &({{ -3}}\quad ,&{{ 5}}) \end{array} \\\quad \\\\ % slope = m slope = \boxed{{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{5-1}{-3-1} \\ \quad \\\\ % point-slope intercept y-{{ y_1}}={{ \boxed{m}}}(x-{{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form}$

recall, the slope-intercept form is just y = mx + b

Answer 2

The equation of the line in the slope-intercept form is $y=-x+2$ such that the line is passing through $(1,1)$ and $(-3,5)$.

Slope

The ratio of the rise and run is knwon as slope.

We will determine the slope of the line first and then substitute it in the equation of the line.

The equation of a line in the slope-intercept form is $y=mx+b$ where,

$y$ is the y-coordinate

$x$ is the x-coordinate

$m$ is the slope of the line

$b$ is the y-intercept

How to determine the equation of a line in the slope-intercept form?

Evaluate the slope of the line as-

$m=\dfrac{y_2-y_1}{x_2-x_1}\\=\dfrac{5-1}{-3-1}\\=\dfrac{4}{-4}\\=-1$

Substitute the value of the slope and one of the two coordinates in the equation of the line to determine the value of the y-intercept.

$y=mx+b\\1=(-1)\times 1+b\\b=2$

Now, substitute the value of the y-intercept and the slope in the slope-intercept of the line as-

$y=(-1)x+2\\y=-x+2$

Thus, the equation of the line in the slope-intercept form is $y=-x+2$.

Learn more about the equation of a line in the slope-intercept form here- https://brainly.com/question/21298390

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