Question - Explanation of Slope-Intercept Form
Solution:
The given equation is the slope-intercept form of a line, which is represented as $$ y = mx + b $$, where:- $$ m $$ is the slope of the line- $$ b $$ is the y-intercept, i.e., the value of $$ y $$ when $$ x = 0 $$There is no specific question to solve, as the image simply provides the general form of a linear equation in slope-intercept form.
Tutor Solution:
The slope-intercept form is a way of writing a linear equation. A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. The slope-intercept form is written as:\[ y = mx + b \]Here, $$ y $$ represents the dependent variable, which means it's the output value that depends on the independent variable $$ x $$.The coefficient $$ m $$ represents the slope of the line. The slope is a measure of how steep the line is, and it's defined as the ratio of the rise (the change in $$ y $$) to the run (the change in $$ x $$). A positive slope means the line is going upward as you move from left to right, while a negative slope means the line is going downward.The constant $$ b $$ represents the y-intercept of the line. This is the point where the line crosses the y-axis. It's the value of $$ y $$ when $$ x $$ is zero.To understand this form thoroughly, consider a practical example. If we have an equation like $$ y = 2x + 3 $$, the slope $$ m $$ is 2, which means for every unit increase in $$ x $$, $$ y $$ increases by 2 units. The y-intercept $$ b $$ is 3, which means when $$ x $$ is 0, $$ y $$ will be 3.The slope-intercept form is particularly useful for graphing linear equations quickly and understanding the relationship between the variables. By knowing the slope and y-intercept, one can plot the y-intercept on the graph and use the slope to determine the direction and steepness of the line.
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