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What is the slope and intercept of \[y = - 3x + 3\]?

seo-qna
Last updated date: 13th Jul 2024
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Answer
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Hint: The equation of a line in slope intercept form is $y = mx + b$ where $m$ is the slope is and $b$ is the $y$-intercept. Arrange the given equation as the form of is slope-intercept using the form rearrange the given equation as the form of slope. In this problem we have to find an intercept of $y$.
Formula used:
Slope- intercept form of a linear equation is
$y = mx + b$,
Where,
$y - y$-coordinate
$m$-slope
$x - x$-coordinate
$b - y$-intercept

Complete step-by-step solution:
The given equation is
$y = - 3x + 3$………………………..(1)
We know that the slope-intercept form is $y=mx+b$................................(2)
The above equation of a line in slope-intercept form. So, here no-need to rearrange the sentence.
Compare the equation (1) and (2),
Where, $m$ is the slope and $b$ is the $y$-intercept value.
Therefore we have,
$m = - 3$
Therefore the slope for this line is $m = - 3$
From these equations (1) and (2) we have $b = 3$
Therefore, the $y$-intercept for this line is $b = 3$ or $\left( {0,3} \right)$
Here the solution for this problem,
Slope is $m = - 3$
$y$-intercept is $b = 3$

Note: Slope: in mathematics the slope or gradient of a line is a number that describes both the direction and the steepness of the line. Slope is calculated by finding the ratio of the vertical change to the horizontal change between two distinct points on a line.
$y$-intercept : In analytic geometry using the common convention that the horizontal axis represents a variable $x$ and the vertical axis represents a variable $y, ay$-interceptor vertical intercept is a point where the graph of a function or relation intersects the $y$-axis of the coordinate system. As such, the points satisfy $x = 0$.
Slope-intercept form: The graph of the linear equation $y = mx + c$ is a line with $m$ and $c$ as $y$-intercept. This form of the linear equation is called slope-intercept form. The values of $m$ and $c$ are real numbers.