The equation of the line is \(\boxed{y \leqslant 3}\) and the passes through the point is \(\left( {0,3} \right).\)
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 \(\left( {{x_1},{y_1}} \right) {\text{and} \left( {{x_2},{y_2}} \right)\) can be expressed as,
\(\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}\)
Given:
The passes through point are \(\left( {0,3} \right){\text{ and }}\left( {1,3} \right).\)
Explanation:
The slope can be obtained as follows,
\(\begin{aligned}m&= \frac{{3 - 3}}{{1 - 0}}\\&= \frac{0}{1}\\&=0\\\end{aligned}\)
Substitute \(0\) for \(m\), \(0\) for \(x\) and \(3\) for \(y\) in equation \(y = mx + c\) to obtain the value of c.
\(\begin{aligned}3 &= 0 \cdot 0 + c\\3&=c\\\end{aligned}\)
Substitute \(3\) for \(c\) and \(0\) for \(m\) in equation \(y = mx + c.y = 3\)
The inequality is either \(y \geqslant 3{\text{ or }}y \leqslant 3.\)
To check whether the equation includes origin substitute 0 for x and 0 for y in equation y \(\leqslant 3,0 \leqslant 3\)
The statement is true. The equation contains origin.
The equation of the line is \(\boxed{y \leqslant 3}\) and the passes through the point is \(\left( {0,3} \right).\)
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: numbers,slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.
