The number is \(\boxed{-12}\) in the inequality \(\boxed{x+4y\geqslant -12}\).
Further explanation:
The linear equation with slope m and intercept c is given as follows.
\(\boxed{y=mx+c}\)
The formula for slope of line with points \(\left({{x_1},{y_1}}\right)\) and \(\left({{x_2},{y_2}}\right)\) can be expressed as,
\(\boxed{m=\frac{{{y_2}-{y_1}}}{{{x_2}-{x_1}}}}\)
Explanation:
The orange line intersects y-axis at \(\left({0,-2}\right)\), therefore the y-intercept is -2.
The orange line intersect the points that are \(\left({1,0}\right)\) and \(\left({0,-2}\right)\).
The slope of the line can be obtained as follows.
\(\begin{aligned}m&=\frac{{-2-0}}{{0-\left(1\right)}}\\&=\frac{{-2}}{{-1}}\\&=2\\\end{aligned}\)
The slope of the line is m = 2.
Therefore, the orange line is \(y\geqslant 2x-2\).
The blue line intersects y-axis at \(\left({0,-3}\right)\), therefore the y-intercept is -3.
The blue line intersect the points that are \(\left({-4,-2}\right)\) and \(\left({0,-3}\right)\).
The slope of the line can be obtained as follows.
\(\begin{aligned}m&=\frac{{-3-\left({-2}\right)}}{{0-\left({-4}\right)}}\\&=\frac{{-3+2}}{4}\\&=-\frac{1}{4}\\\end{aligned}\)
The slope of the line is \(m=-\frac{1}{4}\).
The inequalities is \(x+4y\geqslant b\) passes through the point \(\left({0,-3}\right)\).
\(\begin{aligned}\left(0\right)+4\left({-3}\right)&=b\\-12&=b\\\end{aligned}\)
The number is – 12.
The number is \(\boxed{-12}\) in the inequality \(\boxed{x+4y\geqslant -12}\).
Learn more:
1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear inequalities
Keywords: numbers, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.
