Let
[tex] A(0,1)\\ B(2,0) [/tex]
we know that
The y-intercept is the y-coordinate of the point when the value of x is equal to zero
so
the y-coordinate of the point A is the y-intercept
[tex] y=1 [/tex]
The answer part a) is
The value of y-intercept is [tex] 1 [/tex]
Part b) Find the slope m
we know that
the value of the slope is equal to
[tex] m =\frac{(y2-y1)}{(x2-x1)} [/tex]
Substitute the values
[tex] m =\frac{(0-1)}{(2-0)} [/tex]
[tex] m =-\frac{1}{2} [/tex]
therefore
the answer Part b) is
The value of the slope is equal to [tex] -\frac{1}{2} [/tex]
The general answer is
The slope is [tex] -\frac{1}{2} [/tex]
The value of y-intercept is [tex] 1 [/tex]
The slope of the linear function graphed is [tex]\boxed{ - \frac{1}{2}}[/tex] and the y-intercept is [tex]\boxed1.[/tex]
Further explanation:
The linear equation with slope [tex]m[/tex] and intercept [tex]c[/tex] is given as follows.
[tex]\boxed{y = mx + c}[/tex]
The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right)[/tex] and [tex]\left( {{x_2},{y_2}} \right)[/tex] can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
Explanation:
From the graph it has been observed that the line intersects y-axis at [tex]\left( {0,1} \right).[/tex]
Therefore, the y-intercept of the line is [tex]\boxed1.[/tex]
The line passes through the point [tex]\left( {0,1} \right)[/tex] and [tex]\left( {2,0} \right).[/tex]
The slope of the line can be obtained as follows,
[tex]\begin{aligned}m&=\frac{{0 - 1}}{{2 - 1}}\\&= - \frac{1}{2}\\\end{aligned}[/tex]
The slope of the linear function graphed is [tex]\boxed{ - \frac{1}{2}}[/tex] and the y-intercept is [tex]\boxed1.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: numbers, y-intercept, linear function, graphed, left, intercept form, slope-intercept form, linear equation, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.
